Algebra Examples

$\frac{a^{2} - b^{2}}{a^{2} - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

$\frac{(a + b) (a - b)}{a^{2} - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$

Step 2

Simplify terms.

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Step 2.1

Factor $a$ out of $a^{2} - 3 a$ .

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Step 2.1.1

Factor $a$ out of $a^{2}$ .

$\frac{(a + b) (a - b)}{a \cdot a - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$

Step 2.1.2

Factor $a$ out of $- 3 a$ .

$\frac{(a + b) (a - b)}{a \cdot a + a \cdot - 3} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$

Step 2.1.3

Factor $a$ out of $a \cdot a + a \cdot - 3$ .

$\frac{(a + b) (a - b)}{a (a - 3)} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$

Step 2.2

Factor $2$ out of $2 a - 6$ .

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Step 2.2.1

Factor $2$ out of $2 a$ .

$\frac{(a + b) (a - b)}{a (a - 3)} \cdot \frac{2 (a) - 6}{{(a + b)}^{2}}$

Step 2.2.2

Factor $2$ out of $- 6$ .

$\frac{(a + b) (a - b)}{a (a - 3)} \cdot \frac{2 a + 2 \cdot - 3}{{(a + b)}^{2}}$

Step 2.2.3

Factor $2$ out of $2 a + 2 \cdot - 3$ .

$\frac{(a + b) (a - b)}{a (a - 3)} \cdot \frac{2 (a - 3)}{{(a + b)}^{2}}$

Step 2.3

Combine.

$\frac{(a + b) (a - b) (2 (a - 3))}{a (a - 3) {(a + b)}^{2}}$

Step 2.4

Cancel the common factor of $a + b$ and ${(a + b)}^{2}$ .

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Step 2.4.1

Factor $a + b$ out of $(a + b) (a - b) (2 (a - 3))$ .

$\frac{(a + b) ((a - b) (2 (a - 3)))}{a (a - 3) {(a + b)}^{2}}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $a + b$ out of $a (a - 3) {(a + b)}^{2}$ .

$\frac{(a + b) ((a - b) (2 (a - 3)))}{(a + b) (a (a - 3) (a + b))}$

Step 2.4.2.2

Cancel the common factor.

$\frac{(a + b) ((a - b) (2 (a - 3)))}{(a + b) (a (a - 3) (a + b))}$

Step 2.4.2.3

Rewrite the expression.

$\frac{(a - b) (2 (a - 3))}{a (a - 3) (a + b)}$

Step 2.5

Cancel the common factor of $a - 3$ .

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Step 2.5.1

Cancel the common factor.

$\frac{(a - b) (2 (a - 3))}{a (a - 3) (a + b)}$

Step 2.5.2

Rewrite the expression.

$\frac{(a - b) \cdot (2)}{a (a + b)}$

Step 2.6

Move $2$ to the left of $a - b$ .

$\frac{2 (a - b)}{a (a + b)}$